Control of ramp-up current profile dynamics in tokamak plasmas via the minimal-surface theory

The central task of current profile control during the ramp-up phase of a tokamak discharge is to find the actuator trajectories that are necessary to achieve certain desired current profile at some time between the end of the ramp-up phase and early stage of the flattop phase. The magnetic diffusion partial differential equation (PDE) models the dynamics of the poloidal magnetic flux profile, which is closely related to the toroidal current density profile, and plays a key role in the model-based control synthesis. Given the initial and desired target profiles, splines are used in this work to generate evolutionary curves connecting their boundaries at both endpoints of the spatial domain. Then, a closed four-edge frame (initial profile, target profile, two boundary curves) in the three dimensional space (time, space, poloidal magnetic flux) is obtained without knowing the transient dynamics inside. The minimal surface theory is used in this work to define a surface spanned by the clo...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Chao Xu, Eugenio Schuster
• Keywords: CDC 2009, Closed Four-edge Frame, Control Systems, Poloidal Magnetic Flux, Transient Dynamics